Download 2009 HSC General Mathematics Marking

2009 HSC General Mathematics
Marking Guidelines
Section I
Question
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Correct
Response
C
C
C
A
D
A
A
D
C
B
B
C
B
D
D
A
C
B
B
B
D
A
–1–
2009 HSC
General Mathematics
Marking Guidelines
Section II
Question 23 (a) (i)
Outcomes assessed: P2, P6, P7
MARKING GUIDELINES
Criteria
• Correct equation
Marks
1
Question 23 (a) (ii)
Outcomes assessed: P2, P6, P7
MARKING GUIDELINES
Criteria
• Correct angle
• Significant progress towards finding an angle
Marks
2
1
Question 23 (b) (i)
Outcomes assessed: P10
MARKING GUIDELINES
Criteria
• Correct numerical expression
–2–
Marks
1
2009 HSC
General Mathematics
Marking Guidelines
Question 23 (b) (ii)
Outcomes assessed: P10
MARKING GUIDELINES
Criteria
• Correct numerical expression
Marks
1
Question 23 (c) (i)
Outcomes assessed: H6
MARKING GUIDELINES
Criteria
• Correct area (CNE)
• Significant progress towards finding the area
Marks
2
1
Question 23 (c) (ii)
Outcomes assessed: P2
MARKING GUIDELINES
Criteria
• Correct answer or number of whole boxes
• Progress towards answer
(eg increasing previous answer by 10%)
Marks
2
1
Question 23 (d) (i)
Outcomes assessed: P2
MARKING GUIDELINES
Criteria
• Correct answer
• Significant progress towards finding the result
(eg adding all the fees without the monthly fee)
• Progress towards finding total amount
(eg identifying two fees correctly
OR correctly identifying monthly account fee)
–3–
Marks
3
2
1
2009 HSC
General Mathematics
Marking Guidelines
Question 23 (d) (ii)
Outcomes assessed: P2, P11
MARKING GUIDELINES
Criteria
• Correct answer
Question 24 (a) (i)
Marks
1
Outcomes assessed: P2
MARKING GUIDELINES
Criteria
• Correct answer
Marks
1
Question 24 (a) (ii)
Outcomes assessed: P2
MARKING GUIDELINES
Criteria
• Correct answer OR correct numerical expression
Marks
1
Question 24 (b) (i)
Outcomes assessed: H4
MARKING GUIDELINES
Criteria
• Correct answer
Marks
1
Question 24 (b) (ii)
Outcomes assessed: H4
MARKING GUIDELINES
Criteria
• Correct answer
–4–
Marks
1
2009 HSC
General Mathematics
Marking Guidelines
Question 24 (c)
Outcomes assessed: P11
MARKING GUIDELINES
Criteria
• Correct example with justification
• An age-related facility or service with no reason (e.g. build a preschool)
Marks
2
1
Question 24 (d) (i)
Outcomes assessed: P3
MARKING GUIDELINES
Criteria
• Correct equation
Marks
1
Question 24 (d) (ii)
Outcomes assessed: P5
MARKING GUIDELINES
Criteria
• Correct explanation
Marks
1
Question 24 (d) (iii)
Outcomes assessed: H3, H5
MARKING GUIDELINES
Criteria
• Correct evidence for the comparison
• ONE correct substitution
Marks
2
1
Question 24 (e) (i)
Outcomes assessed: H8
MARKING GUIDELINES
Criteria
• Correct equation with substitution
–5–
Marks
1
2009 HSC
General Mathematics
Marking Guidelines
Question 24 (e) (ii)
Outcomes assessed: H2, H5, H8, H11
MARKING GUIDELINES
Criteria
• Correct statement
• Correct substitution for declining balance equation
–6–
Marks
2
1
2009 HSC
General Mathematics
Marking Guidelines
Question 25 (a)
Outcomes assessed: H3
MARKING GUIDELINES
Criteria
• Correct simplification
• Progress towards correct simplification
Marks
2
1
Question 25 (b)
Outcomes assessed: H7
MARKING GUIDELINES
Criteria
• Correct answer
• Progress towards answer (eg answer in mg)
Marks
2
1
Question 25 (c) (i)
Outcomes assessed: H2, H6
MARKING GUIDELINES
Criteria
• Correct answer OR correct numerical expression
• Significant progress towards
(eg calculation of grass area OR attempt to directly use Simpson’s Rule to
find area of lake with values correct)
• Some progress towards
(eg one application of Simpson’s Rule on grass area
OR correct area of rectangle plus an attempt to use Simpson’s Rule
OR Attempt to directly use Simpson’s Rule to find area of lake with at
least one of the ordinates correct)
–7–
Marks
3
2
1
2009 HSC
General Mathematics
Marking Guidelines
Question 25 (c) (ii)
Outcomes assessed: P6, H2
MARKING GUIDELINES
Criteria
• Correct answer or correct numerical expression
• Progress towards
(eg volume in cubic metres)
–8–
Marks
2
1
2009 HSC
General Mathematics
Marking Guidelines
Question 25 (d) (i)
Outcomes assessed: H9
MARKING GUIDELINES
Criteria
• Correct answer
Marks
1
Question 25 (d) (ii)
Outcomes assessed: H5, H9
MARKING GUIDELINES
Criteria
• Correct answer or correct numerical expression
• Significant progress towards answer
eg correct percentage for one of regions
• Some progress towards answer
eg finding z-score for 38.4
–9–
Marks
3
2
1
2009 HSC
General Mathematics
Marking Guidelines
Question 26 (a) (i)
Outcomes assessed: H4, H9
MARKING GUIDELINES
Criteria
• Correct answer
Marks
1
Question 26 (a) (ii)
Outcomes assessed: H4, H9
MARKING GUIDELINES
Criteria
• Correct answer
Marks
1
Question 26 (a) (iii)
Outcomes assessed: H4, H9
MARKING GUIDELINES
Criteria
• Correct answer
– 10 –
Marks
1
2009 HSC
General Mathematics
Marking Guidelines
Question 26 (b) (i)
Outcomes assessed: H7
MARKING GUIDELINES
Criteria
• Correct numerical expression
• Progress towards answer
Marks
2
1
Question 26 (b) (ii)
Outcomes assessed: H7
MARKING GUIDELINES
Criteria
• Correct answer
Marks
1
Question 26 (b) (iii)
Outcomes assessed: H7
MARKING GUIDELINES
Criteria
• Correct answer including the day
• Progress towards answer (eg Wednesday 6pm)
– 11 –
Marks
2
1
2009 HSC
General Mathematics
Marking Guidelines
Question 26 (c) (i)
Outcomes assessed: H5, H8
MARKING GUIDELINES
Criteria
• Correct answer OR correct numerical expression
Marks
1
Question 26 (c) (ii)
Outcomes assessed: H5, H8
MARKING GUIDELINES
Criteria
• A and B correct OR correct numerical expressions
• Either correct A or significant progress towards B
Marks
2
1
Question 26 (c) (iii) (1)
Outcomes assessed: H5, H8
MARKING GUIDELINES
Criteria
• Correct formula with correct substitution
Marks
1
Question 26 (c) (iii) (2)
Outcomes assessed: H5, H8
MARKING GUIDELINES
Criteria
• Correct answer
– 12 –
Marks
1
2009 HSC
General Mathematics
Marking Guidelines
Question 27 (a) (i)
Outcomes assessed: H8
MARKING GUIDELINES
Criteria
• Correct numerical expression
Marks
1
Question 27 (a) (ii)
Outcomes assessed: H5, H8
MARKING GUIDELINES
Criteria
• Correct numerical expression
Marks
1
Question 27 (a) (iii)
Outcomes assessed: H8, H11
MARKING GUIDELINES
Criteria
• Correct numerical expression
• Significant progress towards
(eg evidence of n and r ie 8.2857)
• Progress towards solution
(eg • conversion of n or r to 1% or 8 periods
• evidence of subtraction of investment)
– 13 –
Marks
3
2
1
2009 HSC
General Mathematics
Marking Guidelines
Question 27 (b) (i)
Outcomes assessed: H6, H7
MARKING GUIDELINES
Criteria
• Correct answer or correct numerical expression
Marks
1
Question 27 (b) (ii)
Outcomes assessed: H6, H7
MARKING GUIDELINES
Criteria
• Correct answer
• Progress towards
(eg an attempt at using the cosine rule)
Marks
2
1
Question 27 (b) (iii)
Outcomes assessed: H6
MARKING GUIDELINES
Criteria
• Correct numerical expression
Marks
1
Question 27 (c)
Outcomes assessed: H4, H10, H11
MARKING GUIDELINES
Criteria
• A clear statement that 0.02 is greater than 0.0199 with correct calculations
obtaining 0.02 and 0.0199
• Significant progress towards answer
(eg correct calculation of both probabilities
OR correct numerical expression)
• Progress towards answer
(eg Mary’s correctly calculated
PLUS progress towards Jane’s probabilities)
• Calculation OR correct numerical expression for Mary
– 14 –
2
100
Marks
4
3
2
1
2009 HSC
General Mathematics
Marking Guidelines
Question 28 (a) (i)
Outcomes assessed: H3, H5
MARKING GUIDELINES
Criteria
• Correct sketch in positive quadrant
Marks
1
Sample answer:
Question 28 (a) (ii)
Outcomes assessed: H3, H5
MARKING GUIDELINES
Criteria
• Correct answer
• Significant progress towards answer, eg finding stopping distance for
70 km/h
Marks
2
1
Question 28 (b) (i)
Outcomes assessed: H4
MARKING GUIDELINES
Criteria
• Correct answer
Marks
1
Question 28 (b) (ii)
Outcomes assessed: H4
MARKING GUIDELINES
Criteria
• Correct equation
• Progress towards, eg finding gradient
– 15 –
Marks
2
1
2009 HSC
General Mathematics
Marking Guidelines
Question 28 (c)
Outcomes assessed: H2, H3, H5
MARKING GUIDELINES
Criteria
• Correct answer or correct numerical expression
• Significant progress towards, eg finding k
• Progress towards, eg stating h = kd2
Marks
3
2
1
Question 28 (d)
Outcomes assessed: H4, H10, H11
•
•
•
•
MARKING GUIDELINES
Criteria
Draws a correct conclusion with correct calculations
Significant progress towards answer
(eg sample space and expected frequencies of differences)
Progress towards answer (eg sample space including differences)
Some progress towards (eg progress towards correct sample space)
– 16 –
Marks
4
3
2
1
General Mathematics 2009 HSC Examination Mapping Grid Question
Marks
Content
Syllabus outcomes
Section I
1
1
PB1
2
1
3
–
The language of chance
P10
AM2 –
Modelling linear relationships
P5
1
DA4 –
Summary statistics
P2, P9
4
1
M4
Right-angled triangles
P2, P6
5
1
DA1 –
Statistics and society
P9
FM2 –
Investing money
6
1
AM4 –
Modelling linear and non-linear
relationships
P2, P8, H2, H5
7
1
PB3
Multi-stage events
H10
8
1
DA5 –
Interpreting sets of data
H4
9
1
PB4 –
Applications of probability
H10
10
1
FM1 –
Earning money
P2
11
1
M5
–
Further applications of area and volume
H6
12
1
M1
–
Units of measurement
P2
13
1
AM2 –
Modelling linear relationships
P3
14
1
AM3 –
Algebraic skills and techniques
H2
15
1
AM3 –
Algebraic skills and techniques
H2
16
1
AM4 –
Modelling linear and non-linear
relationships
H2, H5
17
1
FM5 –
Annuities and loan repayments
H2, H5
18
1
DA2 –
Data collection and sampling
P9
19
1
M2
Applications of area and volume
P6
20
1
FM4 –
Credit and borrowing
H2, H8
21
1
DA4 –
Summary statistics
P2
22
1
M6
–
Applications of trigonometry
H6
23 (a) (i)
1
M4
–
Right-angled triangles
P2, P6, P7
23 (a) (ii)
2
M4
–
Right-angled triangles
P2, P6, P7
23 (b) (i)
1
PB1
–
The language of chance
P10
23 (b) (ii)
1
PB2
–
Relative frequency and probability
P10
23 (c) (i)
2
M5
–
Further applications of area and volume
H6
23 (c) (ii)
2
M1
–
Units of measurement
P2
23 (d) (i)
3
FM1 –
Earning money
P2
23 (d) (ii)
1
FM1 –
Earning money
P2, P11
24 (a) (i)
1
DA3 –
Displaying single data sets
DA4 –
Summary statistics
24 (a) (ii)
1
DA3 –
DA4 –
Displaying single data sets
Summary statistics
P2
24 (b) (i)
1
DA5 –
Interpreting sets of data
H4
–
–
–
Section II
–1–
P2
2009 HSC
Question
General Mathematics
Marks
Mapping Grid
Content
Syllabus outcomes
24 (b) (ii)
1
DA5 –
Interpreting sets of data
H4
24 (c)
2
DA1 –
Statistics and society
P11
24 (d) (i)
1
AM2 –
Modelling linear relationships
P3
24 (d) (ii)
1
AM2 –
Modelling linear relationships
P5
24 (d) (iii)
2
AM3 –
Algebraic skills and techniques
H3, H5
24 (e) (i)
1
FM6 –
Depreciation
H8
FM6 –
Depreciation
24 (e) (ii)
2
AM4 –
Modelling linear and non-linear
relationships
H2, H5, H8, H11
25 (a)
2
AM3 –
Algebraic skills and techniques
H3
25 (b)
2
AM3 –
Algebraic skills and techniques
H7
25 (c) (i)
3
M5
–
Further applications of area and volume
H2, H6
25 (c) (ii)
2
M2
–
Applications of area and volume
P6, H2
25 (d) (i)
1
DA6 –
Applications of normal distribution
H9
25 (d) (ii)
3
DA6 –
Applications of normal distribution
H5, H9
26 (a) (i)
1
DA5 –
Interpreting sets of data
H4, H9
26 (a) (ii)
1
DA5 –
Interpreting sets of data
H4, H9
26 (a) (iii)
1
DA5 –
Interpreting sets of data
H4, H9
26 (b) (i)
2
M7
–
Spherical geometry
H7
26 (b) (ii)
1
M7
–
Spherical geometry
H7
26 (b) (iii)
2
M7
–
Spherical geometry
H7
26 (c) (i)
1
FM4 –
Credit and borrowing
H5, H8
26 (c) (ii)
2
FM4 –
Credit and borrowing
H5, H8
26 (c) (iii) (1)
1
FM5 –
Annuities and loan repayments
H5, H8
26 (c) (iii) (2)
1
FM5 –
Annuities and loan repayments
H5, H8
27 (a) (i)
1
FM5 –
Annuities and loan repayments
H8
27 (a) (ii)
1
FM5 –
Annuities and loan repayments
H5, H8
27 (a) (iii)
3
FM5 –
Annuities and loan repayments
H8, H11
27 (b) (i)
1
M6
–
Applications of trigonometry
H6, H7
27 (b) (ii)
2
M6
–
Applications of trigonometry
H6, H7
27 (b) (iii)
1
M6
–
Applications of trigonometry
H6
27 (c)
4
PB3
–
Multi-stage events
H4, H10, H11
28 (a) (i)
1
AM4 –
Modelling linear and non-linear
relationships
H3, H5
28 (a) (ii)
2
AM4 –
Modelling linear and non-linear
relationships
H3, H5
28 (b) (i)
1
DA7 –
Correlation
H4
28 (b) (ii)
2
DA7 –
Correlation
H4
28 (c)
3
AM4 –
Modelling linear and non-linear
relationships
H2, H3, H5
28 (d)
4
PB4 –
Applications of probability
H4, H10, H11
–2–